If $$y=x^{\sin x}+(\sin x)^x$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{2}$$ is

If $$e^y+x y=e$$ the ordered pair $$\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)$$ at $$x=0$$ is equal to

If $$a$$ and $$b$$ are fixed non-zero constants, then the derivative of $$\frac{a}{x^4}-\frac{b}{x^2}+\cos x$$ is $$m a+n b-p$$, where

If $$y=\left(\cos x^2\right)^2$$, then $$\frac{d y}{d x}$$ is equal to